The split infinitive is another trick of rhetoric in which the ear must be quicker than the handbook. Some infinitives seem to improve on being split, just as a stick of round stovewood does. 'I cannot bring myself to really like the fellow.' The sentence is relaxed, the meaning is clear, the violation is harmless and scarcely perceptible. Put the other way, the sentence becomes stiff, needlessly formal. A matter of ear.
--Strunk and White's The Elements of Style
Exactly. Otherwise, you'd find yourself saying I cannot bring myself, really, to like the fellow.
People haven't spoken like this since the 19th Century.
Heck, the modern era's best-known split infinitive is the line from the opening credits of Star Trek: To boldly go where no man has gone before. Which, of course, is perfect exactly how it is. To go boldly where no man has gone before has no cadence, no rhythm. It sounds awful.
The English language is changing. Almost before our eyes, it is becoming less stuffy, less rigid and more casual. And that silly rule prohibiting split infinitives--which isn't even a rule--is heading for history's dustbin.
Use your ear. It's more reliable.